Detecting Weak but Hierarchically-Structured Patterns in Networks

TL;DR

This paper introduces a hierarchical transform for detecting weak, structured activation patterns in networks, enabling detection of subtle signals and learning network structure from minimal data.

Contribution

It presents a novel hierarchical transform for structured pattern detection and demonstrates its effectiveness and learnability from limited network snapshots.

Findings

Detects very weak activation patterns undetectable by existing methods.

Enables learning of hierarchical network structure from few snapshots.

Provides a sparsifying transform for structured activation patterns.

Abstract

The ability to detect weak distributed activation patterns in networks is critical to several applications, such as identifying the onset of anomalous activity or incipient congestion in the Internet, or faint traces of a biochemical spread by a sensor network. This is a challenging problem since weak distributed patterns can be invisible in per node statistics as well as a global network-wide aggregate. Most prior work considers situations in which the activation/non-activation of each node is statistically independent, but this is unrealistic in many problems. In this paper, we consider structured patterns arising from statistical dependencies in the activation process. Our contributions are three-fold. First, we propose a sparsifying transform that succinctly represents structured activation patterns that conform to a hierarchical dependency graph. Second, we establish that the proposed transform facilitates detection of very weak activation patterns that cannot be detected with existing methods. Third, we show that the structure of the hierarchical dependency graph governing the activation process, and hence the network transform, can be learnt from very few (logarithmic in network size) independent snapshots of network activity.